Can time travel to the past change the present?

The dubious:

This represents a group of scientists that relates time travel with documented,
true and fulfilled prophecies in our own history.
They feel it might be possible that time travel is responsible for the creation of
some of the existing prophecies we know off. Some of these historic prophecies have
found their way into holy books and given rise to religion. The existence of religions
have had an enorm impact on our history. If therefore
time travel is responsible for the existence of religion
then the impact of time travel on our history has been tremendous.

But these scientists might also argue that our past history time line is fixed and cannot be altered.
Each unique 'space-time' event occurs only ones and thereafter this unique event cannot be changed anymore.

Playing with time, and time travel might have impact and cause alterations,
but the consequences will not affect the past, present or future of the scientists.

These scientists might believe in some sort of 'multiple universe theory'
or 'slow correction wave theory'. Anything that could explain why their actions would not
lead to repercussions that will haunt them forever.

They probably try to behave responsibly, as they realise what havoc time travel
technology might cause 'on the other side'.